Solve the following equation using the perfect square trinomial pattern: x2+x+0.25=0
To solve the given equation using the perfect square trinomial pattern, we first rewrite the equation in the form of a perfect square trinomial. For any perfect square trinomial pattern of the form \(x^2 + bx + c\), the pattern is \((x + \frac{b}{2})^2\) or \((x - \frac{b}{2})^2\).
The given equation is \(x^2 + x + 0.25 = 0\).
Take the coefficient of the middle term, which is 1, and divide it by 2: \(\frac{1}{2}\).
Since the sign of the middle term is positive, we use the pattern \((x + \frac{b}{2})^2\).
Plug in the values into the pattern: \((x + \frac{1}{2})^2 = 0\).
To solve for \(x\), we take the square root of both sides: \(x + \frac{1}{2} = \pm \sqrt{0}\).
Simplifying the right side: \(x + \frac{1}{2} = \pm 0\).
Since any number squared is positive, we can conclude that the equation has a single real root at \(x = -\frac{1}{2}\).